Presentation
In the figure bellow, we give an overview of the different research axes of the MUSCLEES team. The horizontal axis distinguishes schematically between the stochastic and deterministic descriptions, while the vertical axis indicates the description scale. At the heart of our research lie the different applications that drive our mathematical studies: living tissues/cell populations, reaction networks and epidemiology (in green in Fig. 1). All our efforts, even the most theoretical ones, will be motivated by biological questions/challenges with applications in these different fields. The MUSCLEES team proposes to tackle these challenges from different and complementary angles, attempting to provide generalizations and unified points of view in the study of biological systems: Axis 2 (in dark red in Fig. 1) is devoted to the understanding of the role of stochasticity in biological systems through the development and analysis of Stochastic Differential Equations (SDE) for reaction networks; Axes 3 and 4 (in blue in Fig. 1) aim to provide a theoretical understanding of continuum models widely used to describe biological systems at the population scale, essentially by use of Ordinary Differential Equations (ODE) for the applications to mathematical epidemiology (dark blue in Fig. 1), or of Partial Differential Equations (PDE) for various applications (in light blue in Fig. 1); and Axis 5, the most interdisciplinary axis of our research team, is entirely devoted to the development of valid agent-based models directly confronted to in vitro/in vivo data for bacterial growth and tissue development and ageing (orange in Fig. 1). Lastly, Axis 1 (in red arrows in Fig. 1) represents one of the fundamental perspectives to link all our research activities. It is devoted to establishing the link between the various modelling viewpoints taken in the other research axes, by deriving, as rigorously as possible, the continuum (ODE, SDE, PDE) models from microscopic agent-based descriptions.
Fig 1. Scheme of the team activities
